A trespassing sign gives information that might not otherwise be known.

The traffic at a library is probably much heavier than the French consulate and the clientele are often juveniles who probably do need to know the rules. This would be more the equivalent of posting such a sign at a business license office

Since a Visa is not required for a visit to France, I assume there would not be frequent long lines of Americans requesting an extended stay in France. As I said I have no problem with a rude person being denied service. It is just seems not very diplomatic to post such a sign.

It also seems a bit arrogant to imply they have the right to deny a Visa to any EU country. If they must have a sign, a simple "we reserve the right to refuse service to the rude and disrespectful." would be sufficient.

It just seems a bit over the top for a country that never misses a chance to lecture on how insulting other cultures is never a good idea.